Question

if each angle of a triangle is less than the sum of the other two show that the triangle is acute​

Answer 1

Answer:

Step-by-step explanation:

Let ∠A<∠B+∠C. Then,

2∠A<∠A+∠B+∠C⇒2∠A<180  degree

⇒∠A<90  degree

Similarly, we obtain ∠B<90  degree

 and ∠C<90  degree

=> Each angle of the triangle is less than 90° and hence it is an acute-angled triangle.

Answer 2

Step-by-step explanation:

Let ∠A<∠B+∠C. Then,

2∠A<∠A+∠B+∠C⇒2∠A<180

∘

⇒∠A<90

∘

Similarly, we obtain ∠B<90

∘

and ∠C<90

∘

=> Each angle of the triangle is less than 90° and hence it is an acute-angled triangle.